Learning soft sensors using time difference-based multi-kernel relevance vector machine with applications for quality-relevant monitoring in wastewater treatment

Considering the time-varying, uncertain and non-linear properties of the wastewater treatment process (WWTPs), a novel multi-kernel relevance vector machine (MRVM) soft sensor based on time difference (TD) is proposed to predict the quality-relevant but difficult-to-measure variable. Firstly, a novel dimension reduction technique is introduced to reduce data dimension and model complexity. Secondly, the parameters of the kernel model are optimized by the intelligent optimization algorithm (PSO). Besides, the TD strategy is introduced to enhance the robustness of MRVM when exposing to dynamic environments. Finally, the proposed model was assessed through two simulation studies and a real WWTP with the results demonstrating the effectiveness of the proposed model. Graphical abstract Framework of Lasso-TD-MRVM soft sensor model.